An ontological characterization of time-series and state-sequences for data mining

Time-series and sequences are important patterns in data mining. Based on an ontology of time-elements, this paper presents a formal characterization of time-series and state-sequences, where a state denotes a collection of data whose validation is dependent on time. While a time-series is formalized as a vector of time-elements temporally ordered one after another, a state-sequence is denoted as a list of states correspondingly ordered by a time-series. In general, a time-series and a state-sequence can be incomplete in various ways. This leads to the distinction between complete and incomplete time-series, and between complete and incomplete state-sequences, which allows the expression of both absolute and relative temporal knowledge in data mining.

Vibrational spectroscopy and DFT calculations of the di-amino acid peptide L-aspartyl-L-glutamic acid in the zwitterionic state

Solid state IR and Raman as well as aqueous solution state Raman spectra are reported for the linear di-amino acid peptide L-aspartyl-L-glutamic acid (L-Asp-L-Glu); the solution state Raman spectrum has also been obtained for the N,O-deuterated derivative. SCF-DFT calculations at the B3-LYP/cc-pVDZ level established that the structure and vibrational spectra of L-Asp-L-Glu can be interpreted using a model of the peptide with ten hydrogen-bonded water molecules, in conjunction with the conductor-like polarizable continuum solvation method. The DFT calculations resulted in the computation of a stable zwitterionic structure, which displays trans-amide conformation. The vibrational spectra were computed at the optimised molecular geometry, enabling normal coordinate analysis, which yielded satisfactory agreement with the experimental IR and Raman data. Computed potential energy distributions of the normal modes provided detailed vibrational assignments.

Vibrational spectra and crystal structure of the di-amino acid peptide cyclo(L-Met-L-Met): Comparison of experimental data and DFT calculations

Experimental Raman and FT-IR spectra of solid-state non-deuterated and N-deuterated samples of cyclo(L-Met-L-Met) are reported and discussed. The Raman and FT-IR results show characteristic amide I vibrations (Raman: 1649 cm-1, infrared: 1675 cm-1) for molecules exhibiting a cis amide conformation. A Raman band, assigned to the cis amide II vibrational mode, is observed at sim1493 cm-1 but no IR band is observed in this region. Cyclo(L-Met-L-Met) crystallises in the triclinic space group P1 with one molecule per unit cell. The overall shape of the diketopiperazine (DKP) ring displays a (slightly distorted) boat conformation. The crystal packing employs two strong hydrogen bonds, which traverse the entire crystal via translational repeats. B3-LYP/cc-pVDZ calculations of the structure of the molecule predict a boat conformation for the DKP ring, in agreement with the experimentally determined X-ray structure. Copyright © 2009 John Wiley & Sons, Ltd.

Vibrational spectroscopy and crystal structure analysis of two polymorphs of the di-amino acid peptide cyclo(L-Glu-L-Glu)

Cyclo(L-Glu-L-Glu) has been crystallised in two different polymorphic forms. Both polymorphs are monoclinic, but form 1 is in space group P21 and form 2 is in space group C2. Raman scattering and FT-IR spectroscopic studies have been conducted for the N,O-protonated and deuterated derivatives. Raman spectra of orientated single crystals, solid-state and aqueous solution samples have also been recorded. The different hydrogen-bonding patterns for the two polymorphs have the greatest effect on vibrational modes with N&bond;H and C&dbond;O stretching character. DFT (B3-LYP/cc-pVDZ) calculations of the isolated cyclo(L-Glu-L-Glu) molecule predict that the minimum energy structure, assuming C2 symmetry, has a boat conformation for the diketopiperazine ring with the two L-Glu side chains being folded above the ring. The calculated geometry is in good agreement with the X-ray crystallographic structures for both polymorphs. Normal coordinate analysis has facilitated the band assignments for the experimental vibrational spectra. Copyright © 2009 John Wiley & Sons, Ltd.